Problem: Solve for $n$, $- \dfrac{n - 10}{n - 9} = \dfrac{1}{9} $
Solution: Multiply both sides of the equation by $n - 9$ $ -(n - 10) = \dfrac{n - 9}{9} $ Multiply both sides of the equation by $9$ $ -9(n - 10) = n - 9 $ $-9n + 90 = n - 9$ $90 = 10n - 9$ $99 = 10n$ $10n = 99$ $n = \dfrac{99}{10}$